Subgroups — C₂×C₁₃×#3212 #15747120

Order 3328.

2218 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3212	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#495	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
18	C₁₃×#532	—	2	4	no	—
19	C₁₃×#532	C₂²	1	8	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₁₃×#529	—	2	4	no	—
23	C₁₃×#529	C₂²	1	8	yes	complemented
24	C₂×C₁₃×#126	—	2	1	no	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	2	yes	—
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#123	—	2	1	no	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	—	2	1	no	—
31	C₂×C₁₃×#121	—	2	1	no	—
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	—	2	1	no	—
35	C₂×C₄×D₄×C₁₃	—	2	1	no	—
36	C₂×C₄×D₄×C₁₃	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	—	2	1	no	—
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#495	C₂²	1	16	yes	complemented
41	C₁₃×#488	C₂²	1	16	yes	complemented
42	C₁₃×#462	C₂²	1	8	yes	complemented
43	C₁₃×#461	C₂²	1	8	yes	complemented
44	C₁₃×#460	C₂²	1	8	yes	complemented
45	C₁₃×#459	C₂²	1	8	yes	complemented
46	C₁₃×#452	C₂²	1	16	yes	complemented
47	C₁₃×#449	C₂²	1	16	yes	complemented
48	C₁₃×#431	C₂²	1	8	yes	complemented
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	2	yes	—
52	C₂×C₁₃×#103	C₂²	1	2	yes	—
53	C₂×C₁₃×#102	C₂²	1	2	yes	—
54	C₂×C₁₃×#102	C₂²	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
56	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
57	C₂×C₁₃×#41	—	2	4	no	—
58	C₂×C₁₃×#41	—	4	4	no	—
59	C₂×C₁₃×#41	—	4	4	no	—
60	C₂×C₁₃×#41	C₂³	1	8	yes	—
61	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	—	2	2	no	—
71	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×Q₁₆	—	4	4	no	—
75	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
76	C₂×C₁₃×SD₁₆	—	4	4	no	—
77	C₂×C₁₃×SD₁₆	—	4	4	no	—
78	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
79	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
80	C₂×C₁₃×D₈	—	4	4	no	—
81	C₂×C₁₃×D₈	C₂³	1	8	yes	—
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	C₂³	1	4	yes	—
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#125	—	2	2	no	—
90	C₁₃×#125	C₂³	1	4	yes	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	4	no	—
93	C₁₃×#124	C₂³	1	8	yes	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
98	C₁₃×#121	—	2	8	no	—
99	C₁₃×#121	—	2	8	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	C₂³	1	4	yes	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
104	C₄×D₄×C₁₃	—	2	8	no	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	2	8	no	—
107	C₄×D₄×C₁₃	—	2	2	no	—
108	C₄×D₄×C₁₃	C₂³	1	4	yes	—
109	C₁₃×#117	—	2	8	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	D₄	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
134	C₁₃×#103	C₂³	1	8	yes	—
135	C₁₃×#103	C₂³	1	8	yes	—
136	C₁₃×#102	C₂³	1	8	yes	—
137	C₁₃×#102	C₂³	1	8	yes	—
138	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
139	C₄×C₈×C₁₃	C₂³	1	8	yes	—
140	C₂×#3212	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₂⁴×C₁₃	—	2	2	no	—
143	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₁₃×#41	—	4	8	no	—
145	C₁₃×#41	—	4	8	no	—
146	C₁₃×#41	—	4	16	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	4	no	—
153	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
154	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	2	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	4	4	no	—
166	C₂×D₄×C₁₃	—	4	4	no	—
167	C₂×D₄×C₁₃	—	4	8	no	—
168	C₂×D₄×C₁₃	—	4	4	no	—
169	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	8	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	—	4	8	no	—
182	C₂²×C₄×C₁₃	—	4	4	no	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₁₃×Q₁₆	—	4	8	no	—
194	C₁₃×SD₁₆	—	4	8	no	—
195	C₁₃×SD₁₆	—	4	8	no	—
196	C₁₃×D₈	—	4	8	no	—
197	C₂×C₈×C₁₃	—	2	4	no	—
198	C₂×C₈×C₁₃	—	2	4	no	—
199	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
200	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	4	no	—
214	C₁₃×C₂²⋊C₄	—	2	8	no	—
215	C₁₃×C₂²⋊C₄	—	2	8	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	C₂×D₄	1	4	yes	—
220	C₄²×C₁₃	C₂×D₄	1	4	yes	—
221	C₄²×C₁₃	C₂×D₄	1	2	yes	—
222	C₄²×C₁₃	C₂×D₄	1	2	yes	—
223	C₄²×C₁₃	C₂⁴	1	2	yes	—
224	C₄²×C₁₃	C₂⁴	1	2	yes	—
225	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#3212	C₂×C₁₃	1	16	yes	direct product factor
228	C₂×#495	C₂×C₁₃	1	2	yes	complemented
229	C₂×#488	C₂×C₁₃	1	2	yes	complemented
230	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₂×#452	C₂×C₁₃	1	2	yes	complemented
235	C₂×#449	C₂×C₁₃	1	2	yes	complemented
236	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	4	4	no	—
243	C₂³×C₁₃	—	4	2	no	—
244	C₂³×C₁₃	—	4	2	no	—
245	C₂³×C₁₃	—	4	4	no	—
246	C₂³×C₁₃	—	4	4	no	—
247	C₂³×C₁₃	—	4	2	no	—
248	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	Q₈×C₁₃	—	2	2	no	—
251	Q₈×C₁₃	—	2	4	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	2	4	no	—
254	Q₈×C₁₃	—	4	2	no	—
255	Q₈×C₁₃	—	4	4	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	4	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	4	no	—
260	D₄×C₁₃	—	4	8	no	—
261	D₄×C₁₃	—	4	8	no	—
262	D₄×C₁₃	—	4	16	no	—
263	D₄×C₁₃	—	4	2	no	—
264	D₄×C₁₃	—	4	4	no	—
265	D₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	8	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	4	4	no	—
279	C₂×C₄×C₁₃	—	4	16	no	—
280	C₂×C₄×C₁₃	—	4	4	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	#135	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
293	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
294	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
295	C₈×C₁₃	—	2	4	no	—
296	C₈×C₁₃	—	2	4	no	—
297	C₂²×#41	C₂²×C₁₃	1	2	yes	—
298	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
299	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
300	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
301	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
302	#532	—	2	4	no	—
303	#532	C₂²×C₁₃	1	8	yes	complemented
304	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
306	#529	—	2	4	no	—
307	#529	C₂²×C₁₃	1	8	yes	complemented
308	C₂×#126	—	2	1	no	—
309	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#124	C₂²×C₁₃	1	2	yes	—
311	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#123	—	2	1	no	—
313	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#121	—	2	1	no	—
315	C₂×#121	—	2	1	no	—
316	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄×D₄	—	2	1	no	—
319	C₂×C₄×D₄	—	2	1	no	—
320	C₂×C₄×D₄	—	2	1	no	—
321	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#117	—	2	1	no	—
323	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
324	#495	C₂²×C₁₃	1	16	yes	complemented
325	#488	C₂²×C₁₃	1	16	yes	complemented
326	#462	C₂²×C₁₃	1	8	yes	complemented
327	#461	C₂²×C₁₃	1	8	yes	complemented
328	#460	C₂²×C₁₃	1	8	yes	complemented
329	#459	C₂²×C₁₃	1	8	yes	complemented
330	#452	C₂²×C₁₃	1	16	yes	complemented
331	#449	C₂²×C₁₃	1	16	yes	complemented
332	#431	C₂²×C₁₃	1	8	yes	complemented
333	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₃	1	2	yes	—
336	C₂×#103	C₂²×C₁₃	1	2	yes	—
337	C₂×#102	C₂²×C₁₃	1	2	yes	—
338	C₂×#102	C₂²×C₁₃	1	2	yes	—
339	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
340	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	2	2	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	4	no	—
346	C₂²×C₁₃	—	4	2	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	4	4	no	—
349	C₂²×C₁₃	—	4	4	no	—
350	C₂²×C₁₃	—	4	2	no	—
351	C₂²×C₁₃	—	8	8	no	—
352	C₂²×C₁₃	—	8	4	no	—
353	C₂²×C₁₃	#535	1	2	yes	—
354	C₂²×C₁₃	C₂×#135	1	2	yes	—
355	C₂²×C₁₃	#575	1	2	yes	—
356	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	4	4	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	2	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	#535	1	2	yes	—
366	C₄×C₁₃	C₂×#135	1	4	yes	—
367	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×#41	—	2	4	no	—
370	C₂×#41	—	4	4	no	—
371	C₂×#41	—	4	4	no	—
372	C₂×#41	C₂³×C₁₃	1	8	yes	—
373	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	—	2	2	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	2	2	no	—
383	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
384	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×Q₁₆	—	4	4	no	—
387	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
388	C₂×SD₁₆	—	4	4	no	—
389	C₂×SD₁₆	—	4	4	no	—
390	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
391	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
392	C₂×D₈	—	4	4	no	—
393	C₂×D₈	C₂³×C₁₃	1	8	yes	—
394	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
395	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
396	C₄⋊Q₈	—	2	2	no	—
397	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
398	#127	—	2	2	no	—
399	#127	C₂³×C₁₃	1	4	yes	—
400	#126	—	2	8	no	—
401	#125	—	2	2	no	—
402	#125	C₂³×C₁₃	1	4	yes	—
403	#124	—	2	2	no	—
404	#124	—	2	4	no	—
405	#124	C₂³×C₁₃	1	4	yes	—
406	#124	C₂³×C₁₃	1	8	yes	—
407	#123	—	2	8	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
410	#121	—	2	8	no	—
411	#121	—	2	8	no	—
412	#121	—	2	2	no	—
413	#121	C₂³×C₁₃	1	4	yes	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
416	C₄×D₄	—	2	8	no	—
417	C₄×D₄	—	2	8	no	—
418	C₄×D₄	—	2	8	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	C₂³×C₁₃	1	4	yes	—
421	#117	—	2	8	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₂²⋊C₄	—	2	2	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄²	D₄×C₁₃	1	4	yes	—
441	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
444	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
445	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
446	#103	C₂³×C₁₃	1	8	yes	—
447	#103	C₂³×C₁₃	1	8	yes	—
448	#102	C₂³×C₁₃	1	8	yes	—
449	#102	C₂³×C₁₃	1	8	yes	—
450	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
451	C₄×C₈	C₂³×C₁₃	1	8	yes	—
452	C₂×C₁₃	—	4	2	no	—
453	C₂×C₁₃	—	8	4	no	—
454	C₂×C₁₃	—	8	2	no	—
455	C₂×C₁₃	#3212	1	4	yes	direct product factor
456	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
457	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
458	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
459	C₂⁴	—	2	1	no	—
460	C₂⁴	—	2	2	no	—
461	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
462	#41	—	4	8	no	—
463	#41	—	4	8	no	—
464	#41	—	4	16	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
472	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	4	4	no	—
484	C₂×D₄	—	4	8	no	—
485	C₂×D₄	—	4	4	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	8	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
511	Q₁₆	—	4	8	no	—
512	SD₁₆	—	4	8	no	—
513	SD₁₆	—	4	8	no	—
514	D₈	—	4	8	no	—
515	C₂×C₈	—	2	4	no	—
516	C₂×C₈	—	2	4	no	—
517	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
518	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₄²	—	2	4	no	—
537	C₄²	C₂×D₄×C₁₃	1	4	yes	—
538	C₄²	C₂×D₄×C₁₃	1	4	yes	—
539	C₄²	C₂×D₄×C₁₃	1	2	yes	—
540	C₄²	C₂×D₄×C₁₃	1	2	yes	—
541	C₄²	C₂⁴×C₁₃	1	2	yes	—
542	C₄²	C₂⁴×C₁₃	1	2	yes	—
543	C₁₃	C₂×#3212	1	1	yes	characteristic, direct product factor, Sylow
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	4	no	—
553	C₂³	—	4	4	no	—
554	C₂³	—	4	2	no	—
555	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	2	4	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	2	4	no	—
561	Q₈	—	4	4	no	—
562	Q₈	—	4	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	8	no	—
569	D₄	—	4	16	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	4	no	—
572	D₄	—	4	8	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	8	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	16	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	8	no	—
592	C₂×C₄	C₁₃×#135	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
599	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
600	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
601	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
602	C₈	—	2	4	no	—
603	C₈	—	2	4	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	8	8	no	—
615	C₂²	—	8	4	no	—
616	C₂²	C₁₃×#535	1	2	yes	—
617	C₂²	C₂×C₁₃×#135	1	2	yes	—
618	C₂²	C₁₃×#575	1	2	yes	—
619	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	4	no	—
627	C₄	—	4	2	no	—
628	C₄	C₁₃×#535	1	2	yes	—
629	C₄	C₂×C₁₃×#135	1	4	yes	—
630	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
631	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂	—	4	2	no	—
633	C₂	—	8	2	no	—
634	C₂	—	8	4	no	—
635	C₂	C₁₃×#3212	1	4	yes	direct product factor
636	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
637	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
638	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#529	C₂	semidirect
3. C₁₃×#3212	C₂	direct (N × H)
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#462	C₂	semidirect
7. C₂×C₁₃×#460	C₂	semidirect
8. C₂×C₁₃×#461	C₂	semidirect
9. C₂×C₁₃×#459	C₂	semidirect
10. C₂×C₁₃×#452	C₂	semidirect
11. C₂×C₁₃×#449	C₂	semidirect
12. C₂×C₁₃×#431	C₂	semidirect
19. C₁₃×#532	C₂²	semidirect
23. C₁₃×#529	C₂²	semidirect
40. C₁₃×#495	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#462	C₂²	semidirect
43. C₁₃×#461	C₂²	semidirect
44. C₁₃×#460	C₂²	semidirect
45. C₁₃×#459	C₂²	semidirect
46. C₁₃×#452	C₂²	semidirect
47. C₁₃×#449	C₂²	semidirect
48. C₁₃×#431	C₂²	semidirect
140. C₂×#3212	C₁₃	direct (N × H)
225. C₂×#532	C₂×C₁₃	semidirect
226. C₂×#529	C₂×C₁₃	semidirect
227. #3212	C₂×C₁₃	direct (N × H)
228. C₂×#495	C₂×C₁₃	semidirect
229. C₂×#488	C₂×C₁₃	semidirect
230. C₂×#462	C₂×C₁₃	semidirect
231. C₂×#460	C₂×C₁₃	semidirect
232. C₂×#461	C₂×C₁₃	semidirect
233. C₂×#459	C₂×C₁₃	semidirect
234. C₂×#452	C₂×C₁₃	semidirect
235. C₂×#449	C₂×C₁₃	semidirect
236. C₂×#431	C₂×C₁₃	semidirect
303. #532	C₂²×C₁₃	semidirect
307. #529	C₂²×C₁₃	semidirect
324. #495	C₂²×C₁₃	semidirect
325. #488	C₂²×C₁₃	semidirect
326. #462	C₂²×C₁₃	semidirect
327. #461	C₂²×C₁₃	semidirect
328. #460	C₂²×C₁₃	semidirect
329. #459	C₂²×C₁₃	semidirect
330. #452	C₂²×C₁₃	semidirect
331. #449	C₂²×C₁₃	semidirect
332. #431	C₂²×C₁₃	semidirect
455. C₂×C₁₃	#3212	direct (N × H)
543. C₁₃	C₂×#3212	direct (N × H)
635. C₂	C₁₃×#3212	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₁₃×#3212	2
C₂×C₁₃×#495	2
C₂×C₁₃×#488	2
C₂×C₁₃×#462	2
C₂×C₁₃×#460	2
C₂×C₁₃×#461	2
C₂×C₁₃×#459	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₁₃×#431	2
C₂×#3212	13

Subgroups — C2×C13×#3212 #15747120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3212 #15747120